I used to share the view that in a negotiation, never make the first offer. The fear is coming in way below as your example indicates. Over time, my attitude changed. I found that by constantly interviewing, I could get a feel for the local market, and have a much better idea of where the ceilings are.
For example over a few years and 3 jobs, I found that $120k was about the max for senior devs in my city and tech stack. When interviewing I would lead with "is 120k in the range for this position?". And getting that could sometimes be a stretch. When I found a company offering 10-15% above that, I took it. I knew they were desperate, and the work would probably suck (and I was right) but no overtime and lot's of vacation make up for it (for now).
For example over a few years and 3 jobs, I found that $120k was about the max for senior devs in my city and tech stack. When interviewing I would lead with "is 120k in the range for this position?". And getting that could sometimes be a stretch. When I found a company offering 10-15% above that, I took it. I knew they were desperate, and the work would probably suck (and I was right) but no overtime and lot's of vacation make up for it (for now).